One of the most fundamental facts in topos theory is the internal parameterization of subtoposes: the bijective correspondence between subtoposes and Lawvere-Tierney topologies. In this paper, we introduce a new but elementary concept, "a local state classifier", and give an analogous internal parameterization of hyperconnected quotients (i.e., hyperconnected geometric morphisms from a topos). As a corollary, we obtain a solution to the Boolean case of the first problem of Lawvere's open problems.
Keywords: Topos, hyperconnected geometric morphism, internal semilattice
2020 MSC: 18B25
Theory and Applications of Categories, Vol. 42, 2024, No. 11, pp 263-313.
Published 2024-08-23.
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